Thanks for the reply. I understand your point, but my question was regarding do Russian. According to my wife, this is used for possession, not for illness. ;)
A couple of examples:
1 - A friend of yours says that his uncle is rich and has everything. Then you would ask: "Что есть у твоего дяди?"
The answer for that would be something like "Oh, he has a private jet, a mustang, a big mansion and so forth"
2 - You are at your friend's uncle's house to fix his TV. You are looking for tools in your bag but you can't find the right one for the job. Then you ask: "Что есть у твоего дяди?"
Hope it helps :)